Question

Let f(x) = 2x and g(x) = √(x − 7). Find and simplify completely

a.) f(3+h)−f(3)/ 8h



b.) g ◦ f)(5)/ (f ◦ f)(3)


for part 8 i have,

2^(3+h) - 2^3/8h = 8*2^h -8 / 8h.

I'm having a brain fart but am i able to subtract 8 from 8 or is the 8*2^h seen as one value, and how can i get rid of the 8h on the bottom.

for part B, i have

√(2^5 − 7) /2^(2^3) = √(32 − 7)/ 2^8 = √25/256 = 5/256.

I posted this question earlier and as the bottom they had it as 64. Im wondering if they were correct with the 64 or am i with the 256?

Answer 1

for part a i messed up. my final result i got is 1/8(2^(3+h) -8)h

Answer 2

(2^(3+h) - 2^3)/(8h)
= (8*2^h -8)/(8h)
= 8(2^h - 1)/(8h)
= (2^h - 1)/h

f(x) = 2^x
g(x) = √(x-7)
(g◦f)(5)/(f◦f)(3)
= √(f(5)-7)/2^(f(3))
= √(2^5-7)/2^(2^3)
= √(32-7)/2^8
= 5/256